Attractor flow

AttractorFlow Skill

You have access to the AttractorFlow MCP server (attractorflow_mcp), which exposes 8 tools for treating agent task execution as dynamical systems rather than reward optimization. The core insight: stop asking "did the agent converge to the right answer?" and start asking "is the agent's trajectory through solution space exhibiting healthy dynamics?"

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Setup

First time in a project:

python3.12 -m venv .venv
.venv/bin/pip install -r attractorflow/mcp-server/requirements.txt

The .mcp.json at project root registers the server automatically. Restart Claude Code after first-time setup to activate MCP tool access.

MCP tool calling — IMPORTANT: AttractorFlow tools (attractorflow_record_state, attractorflow_get_regime, etc.) are called as direct Claude tool calls, not via Bash. They appear in your tool list when the MCP server is connected. Do NOT use Bash to invoke Python scripts for AttractorFlow monitoring — call the tools directly.

Subagent Bash permission: Subagents launched via the Agent tool need Bash access if they also write code. Ensure your session settings allow Bash, or use /attractor-status from the main Claude Code session where MCP is always connected.

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Core Concepts

Lyapunov Exponent (λ) — a single number characterising trajectory health:

• λ < -0.2 → Strongly converging (approaching fixed-point attractor)
• λ ∈ [-0.2, -0.05] → Gently converging (healthy iteration)
• λ ∈ [-0.05, 0.05] → Neutral (limit cycle, plateau, or transition)
• λ ∈ [0.05, 0.25] → Expanding (exploring; OK in design phase only)
• λ > 0.25 or drift_diverging signal → Diverging (intervene now)

Eight Regimes — the classifier maps trajectories to actionable states:

Regime	What it means	λ signal	Action
CONVERGING	Consistent progress toward goal	< -0.05	REDUCE_TEMPERATURE
CYCLING	Healthy dev loop (code→test→fix)	≈ 0, autocorr	CONTINUE (if amp ↓)
EXPLORING	Searching solution space	0.05–0.25	OK in design; pressure in impl
DIVERGING	Drifting from goal	trend > 0 + mean_d > 1	RESTORE_CHECKPOINT
STUCK	Zero progress, fixed-point trap	v ≈ 0, no trend	SPAWN_EXPLORER
OSCILLATING	Alternating between 2 states	lag-1 autocorr < -0.4	BREAK_SYMMETRY
PLATEAU	Slow micro-refinement drift	v ≈ 0, trend < -0.01	NUDGE
UNKNOWN	Insufficient data	< 3 steps	Wait for more data

PLATEAU vs STUCK: both have low velocity. Distinguisher: PLATEAU has a negative distance trend (drifting toward goal in tiny steps). STUCK has no trend. PLATEAU needs a small nudge; STUCK needs a full perturbation or explorer.

Nine Orchestration Actions:

Action	Trigger regime	What to do
CONTINUE	CYCLING (healthy)	Let agent proceed unchanged
REDUCE_TEMPERATURE	CONVERGING	Add to prompt: "Commit to current approach. No alternatives."
INJECT_PERTURBATION	STUCK	Call attractorflow_inject_perturbation, prepend hint to context
SPAWN_EXPLORER	STUCK (deep)	Delegate to explorer-agent subagent
BREAK_SYMMETRY	OSCILLATING	Add asymmetric constraint: write a test only one option passes
RESTORE_CHECKPOINT	DIVERGING	Re-anchor to last checkpoint; re-read original goal
DECOMPOSE_TASK	BIFURCATION	Spawn two subagents, one per discovered cluster
NUDGE	PLATEAU	Add one small specific constraint to unstick the micro-drift
HALT	Any (confidence < 20%)	Stop and ask human for guidance

Bifurcation types:

• PITCHFORK: task splits into 2 symmetric subtasks → spawn 2 parallel agents
• HOPF: direct process becomes iterative → add explicit exit criterion
• SADDLE_NODE: approach collapses → restart from checkpoint with new strategy

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Workflow Pattern

task start
  → attractorflow_record_state(state_text="<first step>", goal_text="<task goal>")
  → [agent does work step by step]
  → after every step: attractorflow_record_state("<what agent just did>")
  → every 3–5 steps: attractorflow_get_regime() → act on action field
  → every 10 steps: attractorflow_detect_bifurcation() → decompose if needed
  → on clean deliverable: attractorflow_checkpoint()
task end

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Intervention Recipes

STUCK → escape sequence:

# Level 1 — add a constraint
attractorflow_inject_perturbation(magnitude=0.3)
# Level 2 — switch tools or approach
attractorflow_inject_perturbation(magnitude=0.6)
# Level 3 — full restart
attractorflow_inject_perturbation(magnitude=1.0)
# OR spawn explorer
use explorer-agent subagent

OSCILLATING → break symmetry:

attractorflow_inject_perturbation(magnitude=0.5)
# Write a specific test that only one option can pass before choosing

DIVERGING → re-anchor:

attractorflow_checkpoint()   # save current position first
# Re-read original goal
# Narrow scope to single most important deliverable

PLATEAU → nudge:

# Add one small specific constraint: a test, a type annotation, a scope limit
# Do NOT inject full perturbation — that overshoots

CYCLING (stable amplitude) → unstick:

attractorflow_inject_perturbation(magnitude=0.4)
# Add a specific new test as deadline

PITCHFORK bifurcation → decompose:

# Spawn subagent A for cluster 1
# Spawn subagent B for cluster 2
# Orchestrator evaluates both, continues with convergent path

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Response Format for /attractor-status

## 🧭 AttractorFlow Status

**Regime:** [REGIME] (confidence: [X]%)
**λ (Lyapunov):** [value] ([converging/neutral/diverging])
**Steps tracked:** [n]

**Diagnosis:** [rationale from classifier]

**Recommended action:** [action]
> [intervention_hint — full text from MCP response]

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When NOT to use AttractorFlow

• Simple one-shot tasks (< 3 steps, no iteration)
• Tasks where the agent is visibly making progress and you have clear success criteria
• Purely informational queries (no code or multi-step work involved)

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Reference Files

• references/dynamical_systems_primer.md — Formal definitions of attractors, Lyapunov exponents, bifurcations